Physics 001.002.023 Fissile or Fusion Nuclear Power

Physics 001.002.023 Nuclear Energy per Nucleon

Alignment

Learning Intentions

By the end of the lesson, students will be able to:

• Explain why fusion can release more energy per nucleon than fission.
• Relate energy released in nuclear reactions to mass defect using .
• Compare the percentage of mass converted into energy in fusion and fission reactions.
• Use binding energy per nucleon to explain why light nuclei release energy through fusion and heavy nuclei release energy through fission.

Success Criteria

By the end of the lesson, students have successfully:

• Described energy release as a result of mass being transformed into energy.
• Calculated energy released per nucleon for fusion and fission examples.
• Explained that fusion releases more energy per nucleon because the mass defect is a greater fraction of the initial mass.
• Used the binding energy per nucleon curve to justify why fusion and fission release energy.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 2: Ionising Radiation and Nuclear Reactions
• Energy and Mass Defect
• Explain that more energy is released per nucleon in nuclear fusion than in nuclear fission because a greater percentage of the mass is transformed into energy.

Phenomenon

The Sun releases enormous amounts of energy every second through nuclear fusion. Nuclear fission reactors also release large amounts of energy, but per nucleon involved, fusion releases more energy than fission.

This raises the question:

Why does joining small nuclei release more energy per nucleon than splitting large nuclei?

Key Idea

Nuclear reactions release energy when the products have less mass than the reactants. The missing mass is called the mass defect and is transformed into energy according to:

Fusion of light nuclei usually converts a greater percentage of the original mass into energy than fission of heavy nuclei. Therefore, fusion releases more energy per nucleon than fission.

Concept

The concept that explains this phenomenon is mass-energy equivalence.

In both fission and fusion, the total mass of the products is slightly less than the total mass of the reactants. This difference in mass is converted into energy.

The important comparison is not only the total energy released, but the energy released per nucleon.

A typical fission reaction releases about , but this energy is shared across about nucleons.

A typical deuterium-tritium fusion reaction releases about , but this energy is shared across only nucleons.

Therefore:

So, even though one fission event releases more total energy than one fusion event, fusion releases more energy for each nucleon involved.

Convention

The key conventions associated with this concept are below.

• Nuclear energy is often measured in electron volts, usually MeV.
• Mass defect is calculated using:

• Energy released is calculated using:

• Energy per nucleon is calculated using:

• A larger percentage mass defect means a larger fraction of the reactant mass has been converted into energy.

Misconceptions

Common misconceptions students have regarding the concept when applying to various situations and solving problems include:

• Fusion always releases more total energy than fission.
• Fission releases less energy because it is a weaker nuclear reaction.
• Energy is created from nothing in nuclear reactions.
• The missing mass disappears rather than being transformed into energy.
• A reaction with a larger total energy release must always release more energy per nucleon.

Further Reading

• Binding energy per nucleon curve
• Mass defect and binding energy
• Nuclear fusion in stars
• Nuclear fission in reactors
• Mass-energy equivalence using

Explicit Instruction

Direct Teaching Sequence

1. Review mass defect:

   • In nuclear reactions, the mass of the products can be less than the mass of the reactants.
   • This missing mass is transformed into energy.

2. Review mass-energy equivalence:

   • A small amount of mass corresponds to a very large amount of energy because is extremely large.

3. Define energy per nucleon:

   • Total reaction energy alone is not enough to compare fission and fusion fairly.
   • We compare energy per nucleon because fission involves hundreds of nucleons, while common fusion reactions involve only a few.

4. Compare fission and fusion:

   • Fission splits a heavy nucleus into medium-sized nuclei.
   • Fusion joins light nuclei into a more stable nucleus.
   • Fusion of light nuclei produces a larger percentage mass defect.

5. Link to binding energy per nucleon:

   • Nuclei become more stable when binding energy per nucleon increases.
   • Fusion increases binding energy per nucleon for light nuclei.
   • Fission increases binding energy per nucleon for very heavy nuclei.
   • The increase per nucleon is generally larger for fusion of light nuclei than for fission of heavy nuclei.

Worked Examples

Worked Example 1

A uranium-235 nucleus absorbs a neutron and undergoes fission. The reaction releases about of energy. The total number of nucleons involved is approximately .

Calculate the energy released per nucleon.

Therefore, the fission reaction releases approximately:

Worked Example 2

A deuterium-tritium fusion reaction is shown below.

Calculate the energy released per nucleon.

The total number of nucleons in the reactants is:

The energy released per nucleon is:

Therefore, this fusion reaction releases:

This is greater than the fission example, even though the total energy released by one fission reaction is larger.

Worked Example 3

Compare the approximate percentage of mass transformed into energy for fission and fusion.

A typical fission reaction releases about from about nucleons.

A typical deuterium-tritium fusion reaction releases about from nucleons.

Using the energy per nucleon values:

Now compare:

The fusion reaction releases about four times more energy per nucleon than the fission reaction.

This means a greater percentage of the original mass is transformed into energy in the fusion reaction.

Check for Understanding

Check 1

A fission reaction releases more total energy than a fusion reaction. Does this mean fission releases more energy per nucleon?

Answer:

No. A fission reaction usually involves hundreds of nucleons, so the energy is shared across many nucleons. Fusion may release less total energy per reaction, but more energy per nucleon.

Check 2

Why does a mass defect lead to energy release?

Answer:

The products have less mass than the reactants. The missing mass has been transformed into energy according to .

Check 3

A fusion reaction releases and involves nucleons. Calculate the energy released per nucleon.

Answer:

Investigation (Alternative to Explicit)

Hypothesis

If fusion produces a greater percentage mass defect than fission, then fusion will release more energy per nucleon than fission.

Data Collection

Students are given a table containing:

• reaction type
• reactant mass
• product mass
• number of nucleons involved
• total energy released

Example data:

Reaction	Energy released	Nucleons involved
Uranium-235 fission
Deuterium-tritium fusion

Students calculate:

• energy released per nucleon
• percentage of mass converted into energy
• comparison between fusion and fission

Analysis

Students complete the following calculations:

Students then answer:

1. Which reaction releases more total energy?
2. Which reaction releases more energy per nucleon?
3. Which reaction converts a greater percentage of mass into energy?
4. Why is energy per nucleon a better comparison than total energy released?

Evaluation

Students evaluate the statement:

“Nuclear fission is more powerful than nuclear fusion because one fission reaction releases more total energy.”

Expected evaluation:

This statement is incomplete. One fission reaction may release more total energy than one fusion reaction, but fusion releases more energy per nucleon because a greater percentage of the original mass is transformed into energy.

Problems

The following problems are designed to help students compare total energy, energy per nucleon, and percentage mass converted into energy.

1. A fission reaction releases and involves nucleons. Calculate the energy released per nucleon.

2. A fusion reaction releases and involves nucleons. Calculate the energy released per nucleon.

3. Compare your answers to Questions 1 and 2. Which reaction releases more energy per nucleon?

4. A nuclear reaction has a reactant mass of and a product mass of .

   a. Calculate the mass defect.

   b. Calculate the percentage of mass converted into energy.

5. A fission reaction has an approximate mass defect of from an initial mass of .

   a. Calculate the percentage of mass converted into energy.

   b. Explain why this percentage is smaller than in many light-nuclei fusion reactions.

6. Explain why the Sun uses fusion, not fission, as its main energy source.

7. Explain the difference between:

   a. total energy released

   b. energy released per nucleon

8. Complete the sentence:

Fusion releases more energy per nucleon than fission because __________.

Problem Answers

3. The fusion reaction releases more energy per nucleon.

4a.

4b.

5a.

5b. The percentage is smaller because the mass defect is a smaller fraction of the total mass involved.

6. The Sun contains mostly light nuclei such as hydrogen. These nuclei release energy when they fuse into heavier nuclei because the products are more stable and have greater binding energy per nucleon.

7. Total energy released is the overall energy produced by one reaction. Energy released per nucleon is the energy divided by the number of nucleons involved, allowing fair comparison between reactions of different sizes.

8. Fusion releases more energy per nucleon than fission because a greater percentage of the original mass is transformed into energy.

Followup

Self-check

Students should be able to answer the following without notes:

• What is mass defect?
• Why does mass defect release energy?
• What does mean?
• Why is energy per nucleon useful?
• Why can fusion release more energy per nucleon than fission?
• Why does a larger percentage mass defect mean a larger energy release per nucleon?

Next Topic

The next topic is a review of nuclear reactions, mass defect, binding energy, and mass-energy equivalence in preparation for problem-solving and exam-style explanation questions.